1,721,073 research outputs found
Strong deflection limit of black hole gravitational lensing with arbitrary source distances
No full textThe gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds pi, gravitational lensing can be analytically approximated by the so-called strong deflection limit. In this paper we remove the conventional assumption of sources very far from the black hole, considering the distance of the source as an additional parameter in the lensing problem to be treated exactly. We find expressions for critical curves, caustics, and all lensing observables valid for any position of the source up to the horizon. After analyzing the spherically symmetric case we focus on the Kerr black hole, for which we present an analytical 3-dimensional description of the higher order caustic tubes
Casimir effect for a perfectly conducting wedge in terms of the local zeta function
No full textThe vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behavior ∼T2 of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string
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